Question

The table shows the total number of pictures Cal took by the end of each week. Cal's Pictures Week (w) Total Number of Pictures 1 4 2 2 8 3 12 4 16 Based on this pattern, which expression can be used to find the total number of pictures Cal took by the end of w weeks?

Answer 1

Let's begin by listing out the given information:

$(x,y)=(1,4),(2,8),(3,12),(4,16)$

From the data given, we will see that the data follows the expression shown below:

$\begin{gathered} Week1\colon\frac{x}{y}=\frac{1}{4} \\ Week2\colon\frac{x}{y}=\frac{2}{8}\Rightarrow\frac{x}{y}=\frac{1}{4} \\ Week3\colon\frac{x}{y}=\frac{3}{12}\Rightarrow\frac{x}{y}=\frac{1}{4} \\ Week4\colon\frac{x}{y}=\frac{4}{16}\Rightarrow\frac{x}{y}=\frac{1}{4} \\ \Rightarrow y=4x \\ \therefore y=4x \end{gathered}$

Therefore, the total number of pictures taken by Cal after w weeks is given by the expression: y = 4x